CCSU Professors

Yuanqian Chen
Helping Students Solve the Mysteries of Math

 

Resolutely upbeat, Dr. Yuanqian Chen, professor of mathematical sciences, is ready when a frustrated student, undergraduate or graduate, bursts out: “I don’t get it. I don’t know what we’re talking about!” She acknowledges the sentiment is always sobering, but admits forthrightly, “As a student myself, I certainly had times when I struggled to understand a new mathematical concept, and I can still identify with my students’ struggles.”

Chen, an Excellence in Teaching award finalist, faces her students’ hurdles gracefully and with a typically sunny disposition. She assures students that understanding mathematics 

in her courses—whether in calculus, linear algebra, logic, trigonometry or graduate-level abstract algebra—doesn’t happen “by magic.” She tells them math is not “something invented to torture the mind” but developed because of a need to solve age-old problems that have a heightened resonance today in science and technology, as well as engineering, medicine, and economics.

Chen’s classroom is a safe haven where she strives to ease “math anxiety.” Soothingly, she asks students to consider objectives, “What are we trying to accomplish, what can we do with this new idea, how is this subject related to what we know?” Students are reassured by seeing directions and connections. “I do not teach mathematics as if it is a toolbox or a recipe book,” she explains. “Before I teach students how to do math, I emphasize why we do math this way. Familiarity with the procedures or formulas is necessary, but it is a disservice to students if we do not convey why such a procedure is applied. Mathematics trains people to think critically and logically and allows them to create their own tools.”

Craig Skigen, who plans to be a teacher himself, called Chen a “gift” and said, “I presented my fears to her because I felt I did not understand the material, and she would still those fears by letting me know I was exactly where I was supposed to be. Her verve for the material helped me sustain a desire to learn throughout the semester.”

In Shanxi, People’s Republic of China, where Chen grew up and went to school, entertaining questions from students was regarded as wasteful of precious lecturing time and considered “improper.” After completing advanced degrees in mathematics from the University of Kansas and joining Central in 1992, Chen vowed to encourage active student participation. “I can improve my teaching by listening to students’ questions,” she concludes. She listens hard, never interrupting as a student stumbles to phrase a question. Because she realizes that “learning to speak mathematics is like learning to speak a new language,” she designed a successful class on the language of first-order logic where students participated actively in analyzing the debate between two well-known mathematicians over the definition of a continuous function.

Since the computer has revolutionized the way mathematics is taught, Chen has integrated technology into her linear algebra classes. “Almost all methods and algorithms introduced in linear algebra need to be implemented by computer programming in practice,” she notes. Thus, she has developed several comprehensive computer projects for linear algebra that go beyond implementing algorithms. These projects allow students to gain a visual understanding of some abstract concepts by bringing the geometric aspects of the math concepts to students. For example, students learn the effects of various linear transformations on geometric figures with the help of MATLAB software. “Students can now discover interesting and important results through experimentation that used to be considered too computationally difficult to do,” explains Chen.

Still, Chen cautions her students. “I don’t want you to think of the computer as a magic box where answers pop up and no analysis is necessary.” To provide students with the experience of analyzing computer errors, she collected several examples where round-off errors caused software failure in solving the problems correctly. “Students were amazed, the computer made a mistake,” exclaims Chen. “My goal is to get them to know what went wrong and how to fix it.”


A Breadth of Careers

The analytical heavy-lifting inherent in learning mathematics prepares students for careers in teaching and in such areas as finance, insurance, actuarial sciences, operations research, and pharmaceuticals. Joseph DiMauro, CCSU Class of 1999 and now a lawyer, says, “I believe the skills I learned from mathematics helped me tremendously. These skills would not have been developed (believe me, at the beginning I was scared and extremely nervous) if Dr. Chen was not the committed teacher that she is.” Conversely, a prospering lawyer enrolled at CCSU to pursue a career in mathematics and computer science. “He was making a lot of money, but he hated his job,” Chen recalls with a hearty laugh. A gifted student, Timothy Brzezinski, who loves mathematics “both for its beauty and application to the real world,” admires Chen’s extensive research dealing with lattice-ordered structures and abstract algebra. Graduate school will be on his horizon, because Chen’s “original and creative teaching style gave me a desire to learn much more about mathematics.”

For all her light-heartedness, Chen engages in scholarship, often dense with complexities and at the forefront of her discipline, entailing research into lattice-ordered algebraic structures, which integrate logic into modern algebra. An intensely modest woman, she blushes deeply as she whispers, “One of my most important results answers a question that had been open since it was raised in 1965.” Then she rushes on, “also, the discovery of a new torsion class and a new way to specify a torsion class.”

Although Chen’s impressive research is not for the intellectually faint of heart—in fact, “even people inside the area may be lost,” she concedes—the professor has not neglected practical applications. She has published papers demonstrating how math can be used to solve problems ranging from error detecting and correcting code in electrical engineering to folding stars in art design, a joint work with Associate Professor of Mathematical Sciences Charles Waiveris.


The Highest Quality

While Chen uses a wide range of resources—including technology and her own enthusiasm—to communicate difficult and abstract notions to students, what makes her an outstanding teacher, according to John Callaghan ’00, is “her patience, her kindness, her encouraging and motivating character, and most of all her availability and willingness to work one-on-one with students. That makes her an individual of the highest quality.”


— Geri Radacsi